• D. M. Gitman
  • I. V. Tyutin
  • B. L. Voronov
Part of the Progress in Mathematical Physics book series (PMP, volume 62)


We call attention to the fact that quantization includes the problem of a correct definition of quantum-mechanical observables like Hamiltonian, momentum, etc. as self-adjoint operators in an appropriate Hilbert space. This problem is nontrivial for systems on nontrivial manifolds or/and with singular interactions. A naïve treatment based on the experience in finite-dimensional algebra or even infinite-dimensional algebra with bounded operators can result in paradoxes and incorrect results. A set of such paradoxes is considered.


Hilbert Space Quantum Mechanic Momentum Operator Symmetric Operator Unbounded Operator 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • D. M. Gitman
    • 1
  • I. V. Tyutin
    • 2
  • B. L. Voronov
    • 2
  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrasil
  2. 2.Department of Theoretical PhysicsP.N. Lebedev Physical InstituteMoscowRussia

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